A typical radar system includes a transmitter, a receiver, and an antenna. After producing a brief radio frequency (RF) pulse, the transmitter is turned off for the receiver to sample echoes. In a radar system, a radio signal of a particular carrier frequency is turned on and off at a pulse repetition frequency rate. The reciprocal of the PRF is the pulse repetition interval (PRI). The required PRI of the radio signal is typically a function of the radar's desired range, because the radio signal has to travel out to the target and reflect back from the target to the receiver again. Longer periods are required for longer range signals, requiring lower PRFs. Conversely, higher PRFs produce shorter unambiguous ranges, but could broadcast more pulses in a given amount of time. These are just a few design trades one must take into account when designing a radar system.
A coherent processing interval (CPI) in radar systems indicates a group of multiple pulses, usually with the same PRF and center frequency. A CPI generally includes multiple coherently integrated pulses. PRF and center frequency are sometimes changed between CPIs or groups of CPIs.
A pulse-Doppler radar is a radar system that determines the range to a target using pulse-timing techniques and uses the Doppler effect of the returned signal to determine the target's velocity. However, range and Doppler measurement of targets for medium PRF radars is negatively affected by having ambiguous ranges and range rates. A key requirement for solving range ambiguities is to know the round-trip time of the transmitted signal and the echo received; the range calculations will remain unambiguous as long as the target is detected before the pulse repetition interval ends. However, if the echo of the transmitted signal is received after the following pulse is transmitted, the round-trip time will be off by one or more PRIs.
The difference between the transmitted time and the time the echo is received, or the round-trip time, is then used to calculate the range. However, if the echo is received after the pulse repetition interval ends and the subsequent pulse is transmitted, the target will appear to have the wrong range based on this calculation. Echoes received in this case are often referred to as multiple time around echoes. The range at which a radar return can be received without receiving multiple time around echoes is referred to as the maximum unambiguous range (Ru). The maximum unambiguous range can be calculated by the following formula:
                              R          u                =                              C            *            PRI                    2                                    (        1        )            
where Ru is the maximum unambiguous range and C is Speed of light.
As shown by the formula, the multiple time around echoes can be eliminated by increasing the PRI long enough to cover the desired range. Using low PRFs would be ideal when trying to cover a long range. However, this is not always feasible during the design of a radar system. At times, PRF switching may be used to resolve range ambiguities in the above-mentioned radar design, which requires the use of multiple PRFs and a resolver algorithm.
A method for solving range ambiguities is therefore required to obtain the target's true range, for instances when the true target's range exceeds Ru. In this instance, the raw return signal from an echo will appear to have a range less than the true target range. This apparent range is a modulo operation of the true range and the PRI.
High and mid PRF radars use methods, such as the Chinese Remainder Theorem (CRT), to solve for range ambiguities. CRT uses multiple PRFs to determine the target's true range. This method declares a range resolved threshold hit after detecting a range coincident threshold hit in at least M of N sequential CPIs. It is often referred to as an M-of-N range resolver. A threshold hit is defined as sufficient energy in a radar return signal that is above some noise threshold to indicate a possible echo of the transmitted signal off of a target. The threshold hit has a range determined based on the round trip time of the echo. A threshold hit is declared when a condition within the received data is met. This condition can be a desired magnitude point above a predefined noise level. A threshold hit represents a potential echo off a target. A threshold hit has a range attribute derived from the round trip time of the echo and potentially other attributes as well, potentially including the magnitude of the echo and its range rate. The threshold hit throughput of an M-of-N range resolver for a radar mode is a major limiting factor in the ability of a radar mode to operate in dense target environments. This impacts the design and implementation of radar modes in high and mid PRF radars. Some prior approaches use small scan areas and/or avoid target dense areas, such as major highways or city streets, to reduce the number of targets.
FIG. 1A depicts threshold hits for a threshold processed radar return in a medium or high PRF radar mode with three targets A, B and C. The threshold hits are presented before range unfolding. As shown, the lengths of the returns for each of the CPIs 1 to N are different reflecting different unambiguous ranges due to a different PRF being employed for each CPI. A range bin typically corresponds to the rate at which the signal is sampled. The depicted threshold hits are associated only with range bins for simplicity, but a threshold hit may have many other parameters not captured in this figure. In some embodiments, a threshold hit may also have a Doppler bin allowing multiple threshold hits per range bin during each CPI interval. In this figure the threshold hits for each CPI are depicted with a number, which is the threshold hit index for that CPI. In this example, the threshold hit indexes are ordered based on the range bin of the range unambiguous return, however, the order is arbitrary and can be different from the depicted order. In this example, targets B and C are detected after the PRI ends and their range is ambiguous.
FIG. 1B shows range unfolded threshold hits in a medium or high PRF radar mode with three targets after range unfolding. The range unfolding process identifies the set of possible true ranges for each of the threshold hits. These new hits are referred to as the range unfolded threshold hits. They are depicted with the threshold hit index from FIG. 1A along with a new number in subscript. The number in subscript is the unfolded range index (e.g., 11, 21, 31, etc.). The unfolded range indexes per CPI range from 1 to the number of times the range is unfolded for that CPI to get to the maximum range of the mode. The unfolded range index of a range unfolded threshold hit is the number of PRIs it would take to transmit a pulse and receive an echo from that range for the given CPI. For example, in CPI2, a return from target A would be received within one PRI, a return from target B would be received within 2 PRIs, and a return from target C would be returned within 3 PRIs, as shown.
FIG. 1E illustrates the range resolved threshold hits which would be output if CPIs 1, 2, and N from FIG. 1B were CPIs processed through an M-of-N range resolver where M and N equal 3. Range resolved threshold hits are found at range bins 10, 29, and 37 because range coincident range unfolded threshold hits occurred at these range bins in 3 (M) of 3 (N) sequential CPIs.
FIG. 1C illustrates an exhaustive state space search for range unfolded threshold hits in the prior N−1 CPIs which are range coincident with range unfolded threshold hit 11 from CPIN in order to identify range resolved threshold hits for an M-of-N range resolver. Such a search must be performed for each of the range unfolded threshold hits in CPIN. Since each hit from CPIN is compared to each of the hits from the prior N−1 CPIs, the required computation scales quadratically with the number of threshold hits. For example, if the number of range unfolded threshold hits per CPI doubled then the number of arrows in FIG. 1C would double indicating that the computation required to process range unfolded threshold hit 11 from CPIN had doubled. This doubling in processing would occur for each of the now doubled range unfolded threshold hits in CPIN. The result would be that the total computation quadrupled when the number of threshold hits per CPI was doubled.
Therefore, there is a need to increase the throughput and thus substantially increase the number of targets which can be detected and tracked by a radar system.